Past projects

Diagnostics of magneto-convection simulations

S. Shelyag (Univ. of Sheffield), M. Schüssler, S.K. Solanki

Fig 1: Image of modulus of the Stokes V parameter integrated over wavelength for the infrared line FeI (15648.5A) as a diagnostic for vertical magnetic field.
Fig 2: Spectrum of Stokes V (circular polarization). The V parameter shows a pronounced signal in the strong flux concentration and a weaker signal where the "slit" traverses a narrow intergranular magnetic flux sheet.

In order to compare the results of magnetohydrodynamical simulations of photospheric magneto-convection with observations, spectral diagnostics is required. We carry out spectral diagnostics of 3-dimensional MHD simulations. The simulations, which include radiative transfer and partial ionization, use a computational box of 6000 x 6000 x 1400 km3 size and an initial vertical magnetic field of 200 G (see Fig 1). The spectral diagnostics is carried out with the STOPRO code (written by S.K. Solanki and C. Frutiger), which calculates Stokes profiles (see, for example, Fig 2) on the basis of the atomic data and the atmospheric parameters like temperature, pressure, magnetic field, and velocity.


  • Stokes diagnostics of simulated solar magneto-convection, Shelyag, S., Schüssler, M., Solanki, S. K., Vögler, A., Astron. Astrophys., 469, 731-747 (2007).
  • G-band spectral synthesis and diagnostics of simulated solar magneto-convection, S. Shelyag, M. Schüssler, S. K. Solanki, S. V. Berdyugina and A. Vögler, Astron. & Astrophys., 427, 335-343, 2004.
  • On the origin of solar faculae, C. U. Keller, M. Schüssler, A. Vögler, and V. Zakharov, Astrophys. J., 607, L59-L62, 2004.
  • Why Solar Magnetic Flux Concentrations Are Bright in Molecular Bands, Schüssler, M., Shelyag, S., Berdyugina, S., Vögler, A., Solanki, S. K., The Astrophysical Journal, Volume 597, Issue 2, pp. L173-L176, 2003.
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    Stability of a magnetic flux tube in helical flow

    F. Kolesnikov, M Schüssler, D, Schmitt

    Figure 1: An unstable flow configuration. The radial component of the velocity was perturbed in the transition layer. The vertical component of the magnetic field is shown in color, arrows represent the perturbation velocity field (initial velocity field is subtracted). The eigen mode with the azimuthal wavenumber m=3 is growing. Onset of the Kelvin-Helmholtz instability of an axisymmetric flux tube in a vortex flow.

    Magnetic flux concentrations in the solar (sub)photosphere are surrounded by strong downflows, which come into swirling motion owing to the conservation of angular momentum. While such a whirl flow can stabilize a magnetic flux tube against the MHD fluting instability, it potentially becomes subject to the Kelvin-Helmholtz and shear instabilities near the edge of the flux tube, which may lead to twisting of the magnetic field and perhaps even to the disruption of the magnetic structure. As a first step towards studying the relevance of such instabilities, we investigate the stability of an incompressible flow with longitudinal and azimuthal (whirl) components surrounding a cylinder with a uniform longitudinal magnetic field. We find that a sharp jump of the azimuthal flow component at the cylinder boundary always leads to a Kelvin-Helmholtz-type instability for sufficiently small wavelengths of the perturbation. On the other hand, a smooth and wide enough transition of the azimuthal velocity towards the surface of the cylinder leads to stable configurations, even for a discontinuous profile of the longitudinal flow.


  • Kelvin-Helmholtz and shear instability of a helical flow around a magnetic flux tube, F. Kolesnikov, M. Bünte, D. Schmitt, and M. Schüssler, Astron. & Astrophys., 420, 737-749, 2004.

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    Dynamics of Magnetic Flux Configurations in the deep Convection Zone

    M. Rempel (HAO, Boulder), M Schüssler

    Color-coded magnetic field strength of a flux sheet after it has exploded due to a buoyancy-driven instability. The horizontal part of the sheet is partly evacuated, leading to a significant increase in field strength. With this mechanism, field-amplification at the base of the convection zone up to 10 Tesla becomes possible within a few months.


  • Intensification of Magnetic Fields by Conversion of Potential Energy, M. Rempel, M. Schüssler, ApJ, 552, pp. L171-L174, 2001.
  • Structure of the magnetic field in the lower convection zone, M. Schüssler, M. Rempel, in A. Wilson (ed.): "From Solar Min to Max: Half a Solar Cycle with SOHO", SOHO 11 Symposium, ESA SP-508, European Space Agency, p. 499, 2002.
  • Storage of magnetic flux at the bottom of the solar convection zone, M. Rempel, M. Schüssler & G. Tóth, Astron. & Astrophys, 363, 789, 2000.

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    Magnetic field reversals and secular variation in a bistable geodynamo model

    D. Schmitt, P. Hoyng (Utrecht), M. Ossendrijver (Freiburg)

    Helicity fluctuations in a mean-field dynamo model lead to a secular variation of the dipole moment and occasionally to sudden polarity reversals. The fluctuations perturb the fundamental dynamo mode, a non-oscillatory dipole, and excite higher modes. This results in stochastic oscillations of the dipole field amplitude in a bistable potential with minima representing normal and reversed polarity, and occasional jumps between them. A relation between the intensity variation and the reversal rate is found, and the observed amplitude distribution of the dipole field is reproduced. The figure displays the toroidal magnetic field as a function of colatitude and time (in units of the diffusion time) with red and blue indicating the two polarities. In the lower panel the dipole amplitude is plotted versus time.


  • A theoretical analysis of the observed variability of the geomagnetic dipole field, P. Hoyng, D. Schmitt, M. A. J. H. Ossendrijver, Phys. Earth Planet. Inter. 130, 143, 2002.
  • Magnetic field reversals and secular variation in a bistable geodynamo model, D. Schmitt, M. A. J. H. Ossendrijver, P. Hoyng, Phys. Earth Planet. Inter. 125, 119, 2001.
  • The geodynamo as a bistable oscillator, P. Hoyng P., M. A. J. H. Ossendrijver, D. Schmitt, Geophys. Astrophys. Fluid Dyn. 94, 263, 2001.

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    Mean-field coefficients for geodynamo models

    M. Schrinner, K.-H. Rädler (Potsdam), D. Schmitt, M. Rheinhardt (Potsdam), U. Christensen

    Large scale magnetic fields in the Earth and other planets, in the Sun and other active stars and also in spiral galaxies are apparently maintained by hydromagnetic dynamos. Concerning the geodynamo there are now dynamo models available that reproduce many features of the Earth's magnetic field very successfully without making any use of mean-field theory. One aim of our work is to compare these results with those based on mean-field theory. This will give an estimation on the reliability and validity of mean-field theory which still is used in dynamo models for various astronomical objects. Within mean-field models the mean-field coefficients a and b are decisive quantities in order to describe dynamo action. We use a dynamically computed velocity field with the aim to calculate mean-field coefficients for the earth's outer core. The 9 components of an a-tensor are shown in the figure on the left. In the other figure, a comparison between direct numerical simualtions and mean-field calculations is presented. While a mean-field model which relies on the full set of determined mean-field coefficients (right, second row) reproduces the azimuthally averaged field given by a direct numerical simulation (right, first row) in great detail, an isotropic approximation for a and b (right, last row) leads to deviations in the amplitudes of the poloidal field and to a different field topology of the induced toroidal field.


  • Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo, M. Schrinner, Rädler, K.-H., Schmitt, D., Rheinhardt, M., Christensen, U.; Geophys. Astrophys. Fluid Dyn., 101, 81 (2007)
  • Mean-field view on rotating magnetoconvection and a geodynamo model, M. Schrinner, K.-H. Raedler, D. Schmitt, M. Rheinhardt, U. Christensen, Astron. Nachr./ AN 326, No. 3/4, 245-249 , 2005.
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    Saturation properties of the Archontis dynamo

    R. Cameron, D. Galloway (Univ. of Sydney)

    This image shows the one-dimensional (orange line) and two-dimensional (color-coded surface) manifolds, as well as heteroclinic orbits (black lines and the one-dimensional manifold) associated with a stagnation point of the Archontis dynamo. The Archontis dynamo is the first known example of a dynamo which, at low resistivity and viscosity, is "Alfvenic" when it saturates (ie the flow everywhere is at the local Alfven speed). Its properties, including the stagnation points, stable and unstable manifolds, and heteroclinic orbits are currently being studied.


  • Saturation properties of the Archontis dynamo, Cameron, R. and Galloway, D., MNRAS, 365, 735-746, 2005.
  • High field strength modified ABC and rotor dynamos, Cameron, R. and Galloway, D., MNRAS, 367, 1163-1169, 2005.

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    Flux tube dynamics in binaries and giant stars

    V. Holzwarth, M. Schüssler

    An erupting flux tube in a model with 1 solar mass at an age of 12.14 Gyr. Subsequent flux tube-configurations are shown until the rising loop has nearly reached the stellar surface. For models with a smaller ratio of core radius to stellar radius the flux tube becomes trapped as the inward directed magnetic tension increases due to geometrical effects. This could explain the decline in X-ray emission of cool giant stars since flux tube-trapping terminates solar-like activity with large bipolar magnetic regions and extended coronal loops.


  • Dynamics of magnetic flux tubes in close binary stars. II. Nonlinear evolution and surface distributions, V. Holzwarth, M. Schüssler, Astron. and Astrophys., 405, 303-311, 2003.
  • Dynamics of magnetic flux tubes in close binary stars. I. Equilibrium and stability properties, 2003, V. Holzwarth, M. Schüssler, Astron. & Astrophys., 405, 291-301, 2003.
  • Do tidal effects determine the spot distribution on active binaries?, V. Holzwarth, M. Schüssler, Astron. Nachr., 323, 3/4, 399-401, 2002.
  • Buried magnetic flux tubes in giant stars near the ``Coronal Dividing Line'', V. Holzwarth, M. Schüssler, Astron. & Astrophys., 377, 251-263, 2001.
  • Stability of magnetic flux tubes in close binary stars, Holzwarth V., Schüssler M., Astron. Nachr., 321, 3, 175-179, 2000.

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    Spatial equilibrium distribution of plasma in rotating dipolar fields

    O. Preuss, V. Holzwarth, S.K. Solanki, M Schüssler

    The search for stable equilibrium distributions of plasma which is trapped in a rotating dipolar field is of interest for many applications in stellar astrophysics, mainly for the problem of magnetically confined circumstellar matter around hot stars. Based on the balance between gravitational and centrifugal forces for a charged particle on a magnetic field line, the picture shows a 3-dimensional visualization of stable (green) and unstable (red) equilibrium positions for an oblique dipolar rotator (i.e., a star with rotation and magnetic dipole axis inclined relative to each other). For the special case of aligned dipole and rotation axes we a stable equatorial disc in agreement with observations of Be stars. If the axes are not aligned, as in the picture, the disc is warped and additional regions of stable equilibrium positions appear.


  • Distribution of magnetically confined circumstellar matter in oblique rotators, O. Preuss, M. Schüssler, V. Holzwarth, and S. K. Solanki, Astron. & Astrophys., 417, 987-992, 2004.

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    Last modified: Mon Sep 17 18:06:42 CEST 2007